One of the biggest challenges facing cosmologists is the nature of dark matter. The cosmological observations, like the rotation curve of galaxies, gravitational weak Lensing and cosmic microwave background radiation indicate that baryonic matter alone cannot explain the density of matter in the Universe. In the context of standard cosmological models, it means that the Universe is made of an unknown component (Dark Matter), which approximately 27% of total energy-momentum. The Modify Gravity and is an alternative theory that is introduced to describe these observations. In This thesis, we introduce the issue of the measurements of accelerated observers in Minkowski space-time that goes beyond the postulate of locality. This is a step towards introducing nonlocal special theory of relativity. Inertia and gravitation are intimately connected in accordance with the equivalence principle. In order to arrive indirectly at a nonlocal gravity, to explain nature of dark matter, we work within framework of teleparallel gravity. Teleparallel gravity is a gauge theory for the translation group and is an alternative theory, fully equivalent to general relativity that renders field equations of gravity in close analogy with Maxwell's equations. This analogy helps us to present Nonlocal gravity. The linear approximation of this theory is thoroughly examined. It is shown that there is a room for dark matter like dynamics in the linear regime. Finally we introduce the gravitational dipole moment to present phenomenology of nonlocal gravity.